When sample sizes are equal (Ji = J), the parameters a1, a2, ... aI of the alternative

Question:

When sample sizes are equal (Ji = J), the parameters a1, a2, ... aI of the alternative parameterization are restricted by (ai = 0. For unequal sample sizes, the most natural restriction is (Ji ai = 0. Use this to show that

What is E(MSTr) when H0 is true? [This expectation is correct if (Jiai = 0 is replaced by the restriction (ai = 0 (or any other single linear restriction on the ai's used to reduce the model to I independent parameters), but (Jiai = 0 simplifies the algebra and yields natural estimates for the model parameters (in particular, a^ = xÌ…i. - xÌ… ..).]